1. Field of the Invention
The present invention relates to an apparatus and a method for channel coding in a mobile communication system, and more particularly to an apparatus and a method for a Low Density Parity Check (LDPC) channel coding in a mobile communication system.
2. Description of the Related Art
Generally, data may be lost due to channel state errors caused by noise, interference and fading when voice and data are transmitted in a wireless mobile communication system. In order to prevent data from being lost, a mobile communication system uses error control techniques. The basic error control technique uses an error control code.
A turbo code and an LDPC code are representative codes of the error control code. The LDPC code not only has a low decoding complexity and can perform a high speed processing through parallel processing, but also exhibits superior performance that can reach the Shannon limit. Accordingly, extensive research is being conducted on the LDPC code as a code suitable for the next generation mobile communication systems.
The LDPC code has been first proposed by Gallager in 1962, but it was not realized by technology of those days even though it exhibits superior performance. The LDPC codes have been rediscovered recently and proved its superior performance with a simple probability decoding method.
The LDPC code is defined by a parity check matrix. The parity check matrix is a matrix in which most of the elements are ‘0’s, which plays a role in determining if received coded signals include errors. Further, the parity check matrix divides an entire parity check matrix into a plurality of partial blocks and allows a permutation matrix to correspond to each of the partial blocks.
The parity check matrix is constructed by a regular method and an irregular method. In the parity check matrix constructed by the regular method, each row and each column have constant weights. However, in the parity check matrix constructed by the irregular method, each row and each column do not have constant weights. The weight represents the number of ‘1’s included in the matrix. In general, the parity check matrix constructed by the irregular method exhibits relatively superior performance or compared to that of the parity check matrix constructed by the regular method. However, because the weights are not constant in the parity check matrix constructed by the irregular method, the weights of each row and each column in the parity check matrix must be properly adjusted in order to ensure superior performance.
FIG. 1A is a diagram illustrating a structure of a parity check matrix of a (3, 6) LDPC code having a coding rate of ½ according to the regular method, and FIG. 1B is a diagram illustrating a parity check matrix when a code length is 1000 bits in FIG. 1A.
The (3, 6) LDPC code represents that six ‘1’s exist in each row and three ‘1’s exists in each column in the parity check matrix.
Referring to FIG. 1A, the parity check matrix includes an information word part 101 mapped with an information word and a parity part 103 mapped with a parity. The numbers ‘3’ within a circle circulating in each of the parts 101 and 103 represent that three ‘1’s exist in each row and each column in the parity check matrix. Because a coding rate of the LDPC code is ½, the information word part 101 must have the same size as that of the parity part 103 in the parity check matrix. A structure of a parity check matrix having a code length of 1000 bits is shown in FIG. 1B.
In a general coding process for an LDPC code, a generation matrix is formed from the parity check matrix, and the data to be transmitted is coded by the generation matrix.
The generation matrix is generated from the parity check matrix by Gaussian elimination. The parity check matrix must satisfy the condition that a multiplication with a received coded signal is ‘0’. Accordingly, the parity check matrix is formed to satisfy the condition as described above. Then, a coding process is performed through matrix multiplication between the data to be transmitted and the generation matrix.
The LDPC code may be expressed on a factor graph. If the LDPC code is expressed on the factor graph, a cycle exists on the factor graph. Iterative decoding on the factor graph in which the cycle exists is sub-optimum in performance. The fact that the LDPC code has superior performance through the iterative decoding has also been experimentally proved. However, when many cycles having short lengths exist on the factor graph, performance of the LDPC code deteriorates due to an error floor. Accordingly, it is preferred to design an LDPC code in which the cycles having the short lengths do not exist on the factor graph.
As described above, the generation matrix is used for the LDPC coding. Because the generation matrix is generated by Gaussian elimination, the number of ‘1’s increases in the generation matrix. An increase in the number of ‘1’s may increase coding complexity for the LDPC code.
In order to solve the above-mentioned problems, various coding methods have been proposed. From among the coding methods, a representative method is a method for minimizing an operation proportional to a square in an operation of restructuring a parity check matrix. However, a coding method capable of remarkably reducing the coding complexity has not yet been developed. Accordingly, it is necessary to develop an LDPC coding method capable of reducing the coding complexity and simultaneously achieving superior performance.